Modification of Mohr's criterion in order to consider the effect of the intermediate principal stress

Abstract

Mohr-Coulomb (M-C) criterion is widely used for isotropic brittle materials, although it has some disadvantages which limit its wider application. One important disadvantage of this theory is that it ignores the effect of the intermediate principal stress, although it has an important influence on materials behaviour. Therefore, Mohr-Coulomb theory is actually used only for materials in biaxial state of stress. In this paper, a modified form of Mohr's criterion has been suggested, in order to overcome this limitation. The modified criterion takes into account the influence of intermediate principal stress in the case of materials under triaxial loading conditions. On the basis of two new hypotheses, a real triaxial state of stress is replaced by a virtual biaxial state of stress. The above mentioned stress states are considered to be equivalent for a material when the failure is imminent in both cases. Both Mohr's theory and the concept of equivalence of stress states are combined in order to obtain the virtual biaxial state of stress, which is determined using all three principal stresses. The modified Mohr's theory can be used only for triaxial state of stress. For biaxial and uniaxial state of stress it is reduced to the classical one. The proposed hypotheses have an important advantage because does not require additional material coefficients. The calculated values using the virtual biaxial state of stress and the linear M-C criterion are in good agreement with experimental data for grey cast iron. The article also presents a compact statistical analysis for both stresses and errors, in order to objectively assess the effectiveness of the formulated hypotheses.